Question

Rakesh is 19 years younger than his father after 5 years their age will be in ratio of 2:3 fond their present age

Answer 1

let rakesh age be x and his fathers age be x+19
5 years hence rakesh=x+5
                       father=x+19+5=x+24
ages in ratio=2:3
so........ x+5:x+24::2:3
=2(x+24)=3(x+5)
=2x+48=3x+15
=2x-3x=15-48
=-x=-33
x=33

Answer 2

GIVEN:-

Rakesh is 19 years younger than his Father.

ratios of their ages after 5 years = 2:3

FIND:-

THEIR PRESENT AGES ?

SOLUTION:-

Let age of Father be x years

$\therefore$ Age of Rakesh = x-19 years

After 5 years

Age of Father = x+5 years

Age of Rakesh = x - 19 + 5 = x - 14 years

ACCORDING TO QUESTION

$\frac{x - 14}{x + 5} = \frac{2}{3}$

$= 3 \times ( x - 14) = 2( x+ 5)$

$= > 3x - 42 = 2x + 10$

$collect \: like \: terms$

$= > 3x - 2x = 10 + 42$

$x = 52$

So, Present age of:

Father = x = 52 years

Rakesh = x -19 = 52 - 19 = 33 years

$so, \: Father\: present \: age \underline{ \boxed{52 \: years}}$

$and \: Rakesh\: present \: age \underline{ \boxed{33 \: years}}$